Problem: Subtract the following rational expressions. $\dfrac{7y^2}{y^3+4y-1}-\dfrac{-2y^2+3y}{y^3+4y-1}=$
We want to subtract two rational expressions whose denominators are equal. We can do this by subtracting the numerators and keeping the denominator the same. [Does this fit with how we subtract rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{7y^2}{y^3+4y-1}-\dfrac{-2y^2+3y}{y^3+4y-1} \\\\ &=\dfrac{(7y^2)-(-2y^2+3y)}{y^3+4y-1} \\\\ &=\dfrac{7y^2+2y^2-3y}{y^3+4y-1} \\\\ &=\dfrac{9y^2-3y}{y^3+4y-1} \end{aligned}$ In conclusion, $\dfrac{7y^2}{y^3+4y-1}-\dfrac{-2y^2+3y}{y^3+4y-1}=\dfrac{9y^2-3y}{y^3+4y-1}$